The proposed work explores the regulatory system that controls the eukaryotic cell division cycle, with an emphasis on the mechanisms that trigger cell-cycle events at the correct time and in the correct order, resulting in robust and accurate reproduction of the cell. The cell-cycle control system is composed of master regulatory enzymes that include the cyclin-dependent protein kinases and a ubiquitin ligase called the anaphase-promoting complex or APC. In the proposed studies, these enzymes and their biological functions will be analyzed using biochemical, cytological, and computational approaches in the budding yeast Saccharomyces cerevisiae. Much of the work will focus on mechanisms of APC activation and substrate binding, which depend on transient association of the APC with a rate-limiting activator subunit that binds the substrate. A previously unknown activity that regulates binding of activator to the APC will be identified and characterized, and single-molecule methods will be developed for analysis of APC-activator interactions. Computational modeling will be used to explore how the modulation of APC-substrate interactions leads to the ordered ubiquitination of APC targets during mitosis. Biochemical approaches will be used to dissect the effects of APC phosphorylation on activator function and to explore activator regulation in the spindle assembly checkpoint. The proposed work also includes studies of the regulation of cell-cycle progression by protein phosphorylation, with an emphasis on the control of late mitotic events by a specific phosphatase. The information gained from these studies will provide important new insights into the control of cell-cycle progression, and will thereby enhance our understanding of diseases, such as cancer, in which cell-cycle control or chromosome segregation is defective. These studies will also illuminate general mechanisms of protein ubiquitination and phosphorylation, regulatory modifications of major importance throughout cell biology and human disease.